ABSTRACT
The failure to recognize a dependence on more than one coordinate scale is a common source of nonuniformity in perturbation expansions. The multiple scale technique can provide a method of rendering these expansions uniform. It is particularly effective in dealing with weakly nonlinear oscillators where the nonlinearity is a small perturbation. The strong nonlinearity in the governing equations of fluid dynamics accounts for some of the difficulties in the mathematical description of turbulence. A problem which has some similarities with turbulence is that of describing the effect of surface roughness in contact phenomena. Surface roughness causes the pressure distribution in a lubricated bearing to have random fluctuations and it is the average pressure which is required. The chapter considers an application of the multiple scale technique to the derivation of an average Reynolds equation which determines the average pressure. It concludes with a description of the Krylov-Bogoliubov technique for dealing with different scales.
